Nyquistcriterion

The Nyquist criterion is a fundamental concept in control theory and signal processing used to determine the stability of a closed-loop system. It is named after Harry Nyquist, a Swedish-American engineer who developed it in the 1930s. The criterion relates the stability of a feedback system to the properties of its open-loop transfer function.

Essentially, the Nyquist criterion analyzes the frequency response of the open-loop system, specifically how the magnitude and phase of the system's output change as the frequency of the input signal varies. This analysis is often visualized using a Nyquist plot, which maps the open-loop transfer function in the complex plane for all frequencies from zero to infinity.

The criterion states that a closed-loop system is stable if and only if the corresponding Nyquist plot of the open-loop transfer function does not encircle the critical point (-1, 0) in the complex plane a certain number of times. The required number of encirclements is determined by the number of poles of the open-loop transfer function in the right-half of the complex plane. A counter-clockwise encirclement of the critical point typically corresponds to a stable pole in the open-loop system, while a clockwise encirclement corresponds to an unstable pole.

By examining the encirclements of the (-1, 0) point, engineers can predict whether a feedback system will become unstable or oscillate when closed. This makes the Nyquist criterion a powerful tool for designing stable and reliable control systems. It is widely applied in various fields, including aerospace, automotive, and industrial automation.